Inner products characterized by difference equations
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- by Gordon G. Johnson PDF
- Proc. Amer. Math. Soc. 37 (1973), 535-536 Request permission
Abstract:
A normed linear space $X$ is an inner product space iff, for some integer $k \geqq 3$, $\sum _{t = 0}^k \binom {k}{t} (-1)^t \left \| a + ab \right \|^2 = 0$ for all $a$ and $b$ in $X$.References
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M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., Heft 21, Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 535-536
- MSC: Primary 46C05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312223-4
- MathSciNet review: 0312223